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Issue 9, 2026
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From the history of physics


Discovery of the relativistic Schrödinger equation

 a,  b,  c,  d
a Department of Applied Mathematics and Statistics, Stony Brook University, New York, New York, USA
b Department of Mathematics, Lamar University, 200 Lucas Building, P.O. Box 10047, Beaumont, TX, 77706, USA
c Landeshauptstadt München, Seminar TMG Universität, Referat für Bildung und Sport, Marienplatz 8, München, 80331, Germany
d School of Mathematical and Statistical Sciences, Arizona State University, P.O. Box 871804, Tempe, AZ, 85287-1804, USA

We discuss the discovery of the relativistic wave equation for a spin-zero charged particle in the Coulomb field by Erwin Schrödinger (presumably during the Christmas holidays of 1925—1926). However, in this new approach, an essential discrepancy was found with the fine structure formula for energy levels already obtained by Sommerfeld in the framework of the 'old' quantum mechanics. As a result, Schrödinger had to withdraw the original 'relativistically framed' article, a draft of which has never been found, from a journal and start all over with his centennial article on the nonrelativistic stationary Schrödinger equation. Our goal here is to follow the original 'relativistic idea' from a modern mathematical viewpoint and elaborate on why Schrödinger did not publish it. We hope that this consideration will encourage readers to study quantum physics at one of the crucial moments of its creation.

Fulltext pdf (885 KB)
Fulltext is also available at DOI: 10.3367/UFNe.2021.06.039000
Keywords: Schrödinger equation, Klein—Fock—Gordon equation, Dirac equation, hydrogen atom, Sommerfeld fine structure formula, Wentzel—Kramers—Brillouin (WKB) approximation, Laplace transform, Nikiforov—Uvarov method
PACS: 01.65.+g, 03.65.−w (all)
DOI: 10.3367/UFNe.2021.06.039000
URL: https://ufn.ru/en/articles/2022/1/e/
000788597000005
2-s2.0-85128558753
2022PhyU...65...90B
Citation: Barley K, Vega-Guzmán Jose, Ruffing A, Suslov S K "Discovery of the relativistic Schrödinger equation" Phys. Usp. 65 90–103 (2022)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 23rd, January 2021, revised: 21st, June 2021, 30th, June 2021

Оригинал: Барли К, Вега-Гузман Х, Руффинг А, Суслов С К «Открытие релятивистского уравнения Шрёдингера» УФН 192 100–114 (2022); DOI: 10.3367/UFNr.2021.06.039000

Shrödinger E is author of Physics-Uspekhi

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